The Non-paraxial Propagation Of Ultra-short Pulsed Beam In Free Space

In this paper, the propagation of the pulsed beam, especially the non-paraxial propagation of the ultrashort pulsed beam is investigated in theory. The paper analyze the paraxial approximation, and the scalar as well as the vectorial non-paraxial correction of the ultrashort pulsed beam are obtained in free space. Then the influence of the spectrum property on the non-paraxial property of the pulsed beam is discussed. The paper is composed of 5 chapters, among which are, Chapter 1 is a survey, Chapter 2,3,4 are the introductions of my own work under the guidence of Prof. Wei Hu in my graduate career.Chapter 1: The development of the investigation about the free-propagation of ultra-short pulsed beam is introduced, and the necessity of the investigation about the non-paraxial propagation of the ultra-short pulsed beam in free space is discussed.Chapter 2: In this chapter, the basic scalar propagation equation of ultra-short pulsed beam in free space is discussed. Based on the basic equation, the non-paraxial correction of pulsed beam is obtained by the spectrum analysis technic and the perturbative technic respectively. The result from the above mentioned two technics are compared to each other. The reliability of the correction is analysed through the comparison bewteen the theoritical and the numerical result.Chapter 3: The influence of vectorial effect on non-paraxial propagation of pulsed beam is analysed based on the basic vectorial propagation equation of ultra-short pulsed beam in free space. On the basis of the analysis and the result of chapter 2, the vectorial non-paraxial correction of ultra-short pulsed beam is obtained.Chapter 4: In this chapter the influence of the spectrum property on the non-paraxial property of the pulsed beam is discussed: Firstly the influence of the spectrum property on the paraxial approximation of pulsed beam is analysed. Then the non-paraxial property of chirped pulsed beam and the variation of the non-paraxial correction induced by the variation of the pulse function are respectively discussed to illustrate the influence of the spectrum property on the non-paraxial property of the pulsed beam.Chapter 5: The conclusion.